2016A&A...585A..98A

We propose a statistical tool to compare the scaling behaviour of turbulence in pairs of molecular cloud maps. Using artificial maps with well-defined spatial properties, we calibrate the method and test its limitations to apply it ultimately to a set of observed maps. We develop the wavelet-based weighted cross-correlation (WWCC) method to study the relative contribution of structures of different sizes and their degree of correlation in two maps as a function of spatial scale, and the mutual displacement of structures in the molecular cloud maps. We test the WWCC for circular structures having a single prominent scale and fractal structures showing a self-similar behaviour without prominent scales. Observational noise and a finite map size limit the scales on which the cross-correlation coefficients and displacement vectors can be reliably measured. For fractal maps containing many structures on all scales, the limitation from observational noise is negligible for signal-to-noise ratios >5. We propose an approach for the identification of correlated structures in the maps, which allows us to localize individual correlated structures and recognize their shapes and suggest a recipe for recovering enhanced scales in self-similar structures. The application of the WWCC to the observed line maps of the giant molecular cloud G333 allows us to add specific scale information to the results obtained earlier using the principal component analysis. The WWCC confirms the chemical and excitation similarity of ¹³CO and C¹⁸O on all scales, but shows a deviation of HCN at scales of up to 7pc. This can be interpreted as a chemical transition scale. The largest structures also show a systematic offset along the filament, probably due to a large-scale density gradient. The WWCC can compare correlated structures in different maps of molecular clouds identifying scales that represent structural changes, such as chemical and phase transitions and prominent or enhanced dimensions.